Journal of Applied Mathematics
Volume 2013 (2013), Article ID 865643, 5 pages
Research Article

Analysis of Average Shortest-Path Length of Scale-Free Network

1Department of Electronic Information and Electric Engineering, Changzhou Institute of Technology, Changzhou 213002, China
2German Research School for Simulation Science, 52062 Aachen, Germany
3Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 4 April 2013; Revised 15 June 2013; Accepted 17 June 2013

Academic Editor: Michael Chen

Copyright © 2013 Guoyong Mao and Ning Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Computing the average shortest-path length of a large scale-free network needs much memory space and computation time. Hence, parallel computing must be applied. In order to solve the load-balancing problem for coarse-grained parallelization, the relationship between the computing time of a single-source shortest-path length of node and the features of node is studied. We present a dynamic programming model using the average outdegree of neighboring nodes of different levels as the variable and the minimum time difference as the target. The coefficients are determined on time measurable networks. A native array and multimap representation of network are presented to reduce the memory consumption of the network such that large networks can still be loaded into the memory of each computing core. The simplified load-balancing model is applied on a network of tens of millions of nodes. Our experiment shows that this model can solve the load-imbalance problem of large scale-free network very well. Also, the characteristic of this model can meet the requirements of networks with ever-increasing complexity and scale.